For \(d=2\) , the number of queries to the oracle needed in order to search for a marked site in a \(d\) -dimensional cubes with \(N\)  sites is \(T=O(\sqrt{N \log N})\)  with flip-flop walk and the moving walk is worse than the classical case. For \(d \ge 3 \) , \(T=O(\sqrt{N})\)  with flip-flop walk and the moving walk is worse than the classical case.
For \( d=1\)  Hadamard quantum random walk, \(T=O(N)\)  with moving walk and flip-flop walk is worse than the classical case [1]}.
